In [1]}, Ekrem and Ulukus studied the vector Gaussian secure source coding problem. and partially characterize the rate-distortion-equivocation function in the case of \(\mu =1\) . However, it seems a difficult task to generalize their source enhancement argument beyond the case of \(\mu =1\) . As pointed out in [2]}, it is also unclear how to generalize the method of factorization in [3]} to handle the non-degraded source. In this section, we proof the extremal inequality based on a novel monotone path construction, and fully characterize the rate-distortion-equivocation function for arbitrary positive \(\mu \) .
